1. Field of the Invention
The present invention relates to control of movement of a wafer stage in one-shot exposure type exposure apparatus (including step-and-repeat type steppers), control of movement of the wafer stage and a reticle stage in exposure apparatus for performing the exposure operation in the reticle scanning method (including step-and-scan type steppers), and control of movement of the wafer stage and a sensor stage in wafer inspecting apparatus for performing inspection in the sensor scanning method and, more particularly, to a method of minimizing the overall turnaround time of stage movement for sequential exposure processes or sequential inspection processes in these apparatus.
2. Related Background Art
For carrying out processes such as exposures or inspections in a wafer provided with plural chip areas, higher production efficiency or inspection efficiency thereof is preferred. Particularly, focusing attention on movement of the stage upon change of chip areas being objects in the predetermined process such as exposure or inspection, the overall turnaround time necessary for the movement of stage through the all chip areas on the wafer needs to be shortened as much as possible. For that, the order of exposures or inspections or the like in the n (n greater than 1) chip areas (i.e., a visit order of the chip areas) needs to be optimized so as to minimize the overall turnaround time necessary for the movement of stage.
For example, supposing that in a one-shot exposure type stepper there are n chip areas to be exposed on the wafer, a conceivable number of movements of the stage between the chip areas is at most nP2=n(nxe2x88x921) (even under the condition that the turnaround time differs depending upon whether the direction of movement of the stage is positive or negative). Accordingly, once the exposure order or the inspection order of the all chip areas is determined, the overall turnaround time necessary for the movement of stage can be obtained uniquely and in short time. However, since there exists n1 ways as to the orders for carrying out the exposures, inspections, or the like of the n chip areas, inordinate time is required for producing and checking the all conceivable orders and for computing all applicable solutions. Particularly, when n greater than 13, it is practically impossible (xe2x80x9cPractical course: Invitation to traveling-salesman problems I, II, III,xe2x80x9d Operations Research 39 (1994), No. 1: pp 25-31, No. 2: pp 91-96, No. 3: pp 156-162).
Further, in the case of the apparatus for carrying out scanning exposure or scanning inspection, typified by the scan exposure type steppers, the reticle stage (or a sensor stage) and the wafer stage need to be controlled in synchronism upon carrying out the exposure, inspection, or the like for each shot area (equivalent to the chip area) on the wafer, and there are degrees of freedom as to scan directions in each shot area. Therefore, the exposure order (exposure sequence) for the all shot areas and the scan directions of local areas (for example, areas successively becoming exposure objects) in the respective shot areas must be optimized simultaneously. The number of conceivable exposure sequences or inspection sequences (either of which is included in the movement sequence) is given by the product of the number of combinations with the scan directions of local areas in the respective n shot areas (if the degrees of freedom of the scan directions are m, the number of combinations is re) and the number of permutation of exposures (or inspections) of the n shot areas (n!), i.e., mnxc3x97n!. It is thus more difficult to obtain an optimum solution of movement sequence than in the case of the one-shot exposure type steppers.
In the conventional apparatus described above, therefore, optimum simultaneous control sequences of the wafer stage and reticle stage to minimize the turnaround time of exposure sequence under specific conditions anticipated are preliminarily set in order to shorten the time for successive exposures of plural areas on the wafer within practical computation time. When an actual operation condition does not suit the above specific conditions, only an unfit portion of the optimum simultaneous control sequences preset is modified so as to fit the above specific conditions. Accordingly, recomputation of optimum movement sequences is not carried out each time in the practical operations.
The inventor examined the conventional technology described above and found the following problems.
First, the conventional apparatus such as the one-shot exposure type steppers cannot obtain an optimum or near-optimum solution to a permutational optimization problem within short time. An ideally preferred way is such that movement sequences to indicate orders of exposures, inspections, or the like in the chip areas are generated and examined and among them a movement sequence having the shortest time is determined as a solution of movement sequence to be found. However, studying what order should be employed for the exposures, inspections, or the like in the n chip areas provided on the wafer, even the one-shot exposure type steppers require examination of n! movement sequences for only exposure orders or inspection orders of n chip areas. In particular, when n greater than 13, inordinate time is consumed for the computation of solution so that it practically seems impossible to obtain the solution. Therefore, for increasing the throughput, effective generation of optimum or near-optimum solution is necessary as to the exposure order or inspection order.
Second, the conventional apparatus such as the steppers of the scan exposure type requires more considerable time for obtaining the optimum or near-optimum solution to the composite problem of the permutational optimization problem with the combinatorial optimization problem. Since the apparatus for carrying out the scanning exposure or scanning inspection, typified by the scan exposure type steppers, has the degrees of freedom as to the exposure order or the inspection order of each chip area on the wafer and as to the scan directions of local areas in the respective chip areas, simultaneous optimization of these must also be considered. Since the optimization of exposure sequence and the optimization of scan direction on the wafer are correlated with each other, they cannot be so managed that the optimization of scan direction is carried out after the optimum solution of exposure sequence has been obtained. Conversely, they cannot be so managed that the optimization of exposure sequence is carried out after the optimum solution of scan direction has been obtained, either. In this case, the number of combinations of permissible scan directions for the all n chip areas is the n-th power of the degrees of freedom of scan directions: m (e.g., m=2 in the scan exposure type steppers); concerning movement sequences of two stages taking account of both movement of the wafer stage and movement of the reticle stage or the sensor stage (scanning of local area in each chip area), the number of conceivable movement sequences is mnxc3x97n!. It is thus practically impossible to perform generation of the all movement sequences or to perform all probable inspections. In order to increase the throughput, efficient generation is also necessary for the optimum or near-optimum solution of exposure sequence.
Third, the above problems must be solved even if the user gives an instruction of an arbitrary constraint in practical operations. Examples of the constraint given by the user include such constraints that no exposure should be effected in one shot area or two or more shot areas (process object regions) selected by the user, that the scan direction in one shot area or two or more shot areas selected by the user should follow the instruction given by the user, and so on. In practical operations the above problems must be solved even under the operation conditions to which the arbitrary constraint is added, as described. In the operation of the above conventional apparatus, however, even if such a constraint is given, a corrective solution to satisfy the constraint thus added is generated by partly modifying a solution of exposure sequence preliminarily obtained under the specific conditions. This provides no guarantee that the corrective solution generated is optimum or good in quality under the above arbitrary constraint condition. Accordingly, in order to increase the throughput, even if the user gives the instruction of the arbitrary constraint, it is necessary to develop and apply an algorithm for efficiently generating the optimum or near-optimum solution, as described in the foregoing description of problem, out of constraint-satisfying solutions (feasible basic solutions) satisfying the constraint.
Fourth, in practical operations, a trade-off needs to be taken into account between the allowed computation time for generating the optimum or near-optimum solution, and the quality of solution generated. In the case of the apparatus for carrying out the scanning exposure or the scanning inspection, typified by the scan exposure type steppers, in order to determine the exposure sequence of each chip area, the object is only to find an approximate solution within short time limited because of enormous computation. The computation to obtain the optimum solution of exposure sequence is conducted upon exchange of reticles of different exposure patterns, upon exchange of wafers, for example, from the reason that unexposed portions are designated randomly for each of the individual wafers though an identical exposure pattern is applied, and so on. Therefore, the allowed computation time varies depending upon the cases. For example, the time necessary for replacement of reticle and alignment of the reticle (reticle loading time) is approximately 20 seconds, and the time for replacement of wafer and alignment of the wafer (wafer loading time) is approximately 10 seconds. Further, if the load on a computer is high during alignment, the computation to obtain the optimum solution of exposure sequence must be conducted within wafer replacement time (for example, one second or so).
An object of the present invention is, therefore, to provide a movement sequence determining method for achieving a preferred solution of movement sequence within short time and an apparatus for realizing it. The movement sequence determining method according to the present invention is a method of, upon executing a predetermined process of exposure, inspection, or the like on a wafer or the like, first obtaining within a very short time a near-optimum solution of a movement sequence (for examples including an exposure sequence or an inspection sequence) to shorten turnaround time necessary for the entire process, then successively generating solutions to further shorten the overall turnaround time of movement sequence as far as computation time allows, and finally generating an optimum solution (if a sufficient, allowed computation time is given). This can provide a solution with quality consistent with the allowed computation time given (a better solution with a longer allowed computation time), depending upon the circumstances of available computation resources.
The movement sequence determining method according to the present invention is a movement sequence determining method that can determine within short time both an order of exposure processes or inspection processes of all chip areas and scan directions of successively exposed or inspected areas in the respective chip areas (hereinafter referred to as scan directions of local areas), mainly, for a plurality of process areas (chip areas) on a surface of a wafer exposed or inspected with scan in a specific direction (one direction selected from finite directions) along the surface of the wafer being a photosensitive substrate. The movement sequence determining method according to the present invention can be applied not only to the scanning exposure type steppers involving movement between chip areas (movement of the wafer stage) and scanning of local area in each chip area (movement of the reticle stage or the sensor stage), but also to the one-shot exposure type steppers.
In particular, in order to solve the above problems, the movement sequence determining method according to the present invention comprises an arithmetic step of obtaining a solution of movement sequence most preferred with respect to a total movement time between plural chip areas (or an overall turnaround time necessary for the process of exposure, inspection, or the like including movement between the chip areas), using at least one of a method based on operations research technique and an evolutionary computation method (including genetic algorithm). This arithmetic step comprises at least a first step of generating a group including a plurality of movement sequences capable of being carried out, out of a group of movement sequence candidates, each indicating scan directions of local areas in the plural chip areas and a process order (visit order) of the plural chip areas, and a second step of selecting a movement sequence in which the movement operation between the plural chip areas (the overall turnaround time necessary for the predetermined process also including the movement between chip areas) is completed within the shortest time, out of the group generated. The above arithmetic step can also be carried out plural times, thereby a most preferred solution of movement sequence at that time can be obtained every completion of arithmetic step. In the second step of the above arithmetic step, the size of a pattern region formed on the mask and the size of the substrate are also taken into account as information concerning the mask (reticle) and the wafer (photosensitive substrate).
Specifically, the movement sequence determining method according to the present invention comprises a prestep of producing a movement time management table in which times necessary for movement between chip areas are recorded, prior to the arithmetic step, in order to decrease the turnaround time of the above arithmetic step.
The optimum solution of movement sequence must be determined also taking account of the scan directions of local areas each processed in each chip area on the wafer. In practical operations there could occur cases wherein scanning is permitted only in one direction or in plural directions, depending upon the chip areas. Therefore, the above movement time management table stores the movement times, each being necessary for movement from a scan end position in a chip area after completion of the process of exposure or the like to a scan start position in each of chip areas to which the exposure light is allowed to move. This movement time management table also includes information about inhibition of movement from a scan end position in one chip area to a scan start position in another chip area, for all combinations of chip areas between which the exposure light is not allowed to move. As also seen from this, the above movement time management table also includes the information concerning the scan directions of local areas in the respective chip areas, in addition to the information concerning the movement order of each chip area.
The movement sequence determining method according to the present invention uses a genetic algorithm (which is one of evolutionary computation methods) as a search technique for a good solution or an optimum solution of movement sequence to be found, in the above arithmetic step, or takes into the genetic algorithm (GA) an improving search technique as a genetic operator, such as a method based on operations research technique (including at least one of a linear programming method (NN method), an algorithm by Lin and Kernighan (S. Lin and B. W. Kernighan, An Effective Heuristic Algorithm for the Traveling Salesman Problem, Operations Research 21 (1973) pp 498-516), or a k-OPT method (including the 2-OPT method and the 3-OPT method) (xe2x80x9cpractical course: Invitation to traveling salesman problems I, II, III,xe2x80x9d Operations Research 39 (1994), No. 1: pp 25-31, No. 2: pp91-96, No. 3: pp 156-162), thereby a best movement sequence out of the solutions obtained at that time is always presented even on the way of computation for obtaining the optimum solution of movement sequence. Further, this search technique can attain a better movement sequence with more time for computation, and is thus characterized in that it can obtain a movement sequence with good quality consistent with the allowed computation time even when computation is interrupted or even when the computation time is preliminarily limited.
For maintaining diversity in the movement sequence candidate group produced in the above arithmetic step, the genetic algorithm has a mutation operator. This mutation operator has at least one of an operator (Cyclic Shift) for exchange of movement order (visit order) of plural chip areas selected out of the plural chip areas, and an operator (Direction Flip) for inversion of scan direction in one chip area or two or more chip areas selected out of the plural chip areas.
Further, the movement sequence determining method according to the present invention can also utilize, as a search technique for a best or optimum solution of movement sequence carried out in the above arithmetic step, one of the operations-research-like techniques such as the linear programming method, the Lin and Kernighan""s algorithm, or the k-OPT method, and combinations thereof.
As for generation of an initial solution, for example, in the case of the above linear programming method, a possible arrangement is such that when there exists a plurality of near-optimum solutions as to a movement sequence to be found, a plurality of good solutions are generated by recalculation by a different method for selecting a specific one or by recalculation with a different search start point and a good solution most preferred with respect to the total movement time between the plural chip areas out of these plural good solutions generated is set as an initial solution of the genetic algorithm. In the case of the combinations of the above approaches including the linear programming method, a possible arrangement is such that a plurality of first good solutions obtained by the linear programming method for the movement sequence to be found are used as initial solutions, a plurality of second good solutions are generated therefrom by the Lin and Kernighan""s algorithm or the k-OPT method, and a second good solution most preferred with respect to the total movement time between the plural process areas out of the plurality of second good solutions thus generated is set as an initial solution of the genetic algorithm.
The movement sequence determining method according to the present invention can be carried out in the exposure apparatus or the inspection apparatus described previously and, in this case, the apparatus has an arithmetic section for carrying out the above arithmetic step and comprises at least a memory for storing the above table.
As described above, the movement sequence determining method according to the present invention continuously generates good solutions of movement sequence successively improved and updated in the algorithm, using the evolutionary computation method (including the genetic algorithm). Further, for the plural process areas (n chip areas), the genetic algorithm is utilized as a search technique for the optimum solution in order to obtain the optimum solution of movement sequence (a candidate to minimize the overall turnaround time in the candidate group) for processing the all process areas, out of the movement sequence candidate group of combinations (ma) of the process area visit orders (n! ways) for processing the all process areas and the scan directions (m degrees of freedom) of local areas in the respective process areas. Each of genes in the genetic algorithm is made to simultaneously store scan directions of the reticle (or the sensor) (note: scanning of the reticle or the like corresponds to scanning of the exposed or inspected local area in each process area on the wafer) and an exposure (inspection) order of the object (the photosensitive substrate such as the wafer), thereby the optimum solution of movement sequence can be generated also taking account of change in the position of the object (start/end point of exposure or inspection) depending upon the scanning of the reticle (or the sensor) and thereby the optimum and near-optimum solutions can be generated taking account of synchronization of the two moving stages on the object (chip area) side and on the reticle side (sensor side). The genetic algorithm is used, for example, as an approach for the case to find the shortest path in visiting all cities only once, but there has been and is no example of application to the apparatus such as steppers in order to optimize exposure (inspection) paths of chip areas on the wafer.
In addition, the present invention adopts the principle of the genetic algorithm, which is a principle to successively generate near-optimum solutions by two features; (1) simultaneous progress of a local search and a global search in the space of interest by a combination of a crossover operator with a mutation operator; and (2) alteration of generation for repetitively carrying out a series of operations for objects of finite genes including the best gene of each generation, one generation being defined as a series of operations by the genetic operators; and to finally obtain the optimum solution. Therefore, the near-optimum solution or the optimum solution can be efficiently generated with depending upon the turnaround computation time.
Considering applications to a positioning device of the reticle (or sensor) scanning type, the scan directions of local areas and the exposure (inspection) order of objects are simultaneously stored in each of the genes in the genetic algorithm, whereby the optimum solution can be generated also taking account of change in the position of object (start/end point of exposure or inspection) depending upon the scanning of the reticle (or the sensor) and whereby the optimum and near-optimum solutions can be generated efficiently taking account of synchronization of the two moving stages on the object side and on the reticle (sensor) side.
Since the information stored in each gene is the length depending upon the number of chip areas as objects in the process of exposure, inspection, or the like, when an unnecessary region of exposure (or inspection) is designated optionally, a necessary operation is only changing the information stored in the gene and the algorithms such as the genetic operators and the alteration of generation can be used as they are. In the case wherein there is a constraint of scan direction in each chip area, the optimum solution can be searched out of constraint satisfying solutions by eliminating genes having information not satisfying the constraint upon alteration of generation.
The present invention will be more fully understood from the detailed description given hereinbelow and the accompanying drawings, which are given by way of illustration only and are not to be considered as limiting the present invention.
Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will be apparent to those skilled in the art from this detailed description.